Franz Franchetti, Markus Püschel, Yevgen Voronenko, Srinivas Chellappa and José M. F. Moura (IEEE Signal Processing Magazine, special issue on ``Signal Processing on Platforms with Multiple Cores'', Vol. 26, No. 6, pp. 90-102, 2009)
Discrete Fourier Transform on Multicores: Algorithms and Automatic Implementation
Preprint (453 KB)
Published paper (link to publisher)

This paper gives an overview on the techniques needed to implement the discrete Fourier transform (DFT) efficiently on current multicore systems. The focus is on Intel compatible multicores but we also discuss the IBM Cell, and briefly, graphics processing units (GPUs). The performance optimization is broken down into three key challenges: parallelization, vectorization, and memory hierarchy optimization. In each case, we use the Kronecker product formalism to formally derive the necessary algorithmic transformations based on a few hardware parameters. Further code level optimizations are discussed. The rigorous nature of this framework enables the complete automation of the implementation task as shown by the program generator Spiral. Finally, we show and analyze DFT benchmarks of the fastest libraries available for the considered platforms.

Learn the current Spiral system, Multithreading, Algorithm theory and analysis, SIMD vectorization, SPIRAL program generation system for transforms, Spiral overview paper, Discrete/fast Fourier transform, Fast algorithms, Parallel processing